Systems and methods for joint demodulation and demapping

ABSTRACT

A method for wireless communication is described. The method includes receiving a signal that is pattern-mapped and Gaussian frequency-shift keying (GFSK) modulated. The method also includes performing a joint demapping and demodulation of the received signal based on a stored accumulated phase. The method may further include updating the stored accumulated phase based on the joint demapping and demodulation.

TECHNICAL FIELD

The present disclosure relates generally to wireless communications.More specifically, the present disclosure relates to systems and methodsfor joint demodulation and demapping.

BACKGROUND

In the last several decades, the use of electronic devices has becomecommon. In particular, advances in electronic technology have reducedthe cost of increasingly complex and useful electronic devices. Costreduction and consumer demand have proliferated the use of electronicdevices such that they are practically ubiquitous in modern society. Asthe use of electronic devices has expanded, so has the demand for newand improved features of electronic devices. More specifically,electronic devices that perform functions faster, more efficiently orwith higher quality are often sought after.

Some electronic devices communicate with other electronic devices. Theseelectronic devices may transmit and/or receive electromagnetic signals.For example, a smartphone may transmit signals to and/or receive signalsfrom another device (e.g., a laptop computer, an electronics console ina vehicle, a wireless headset, etc.). In another example, a wirelessheadset may transmit signals to and/or receive signals from anotherdevice (e.g., a laptop computer, a game console, a smartphone, etc.).

However, particular challenges arise in wireless communications. Forexample, some wireless communication devices may have a limited range.This limited range may lead to connectivity problems and unsatisfactoryperformance in some situations. As can be observed from this discussion,systems and methods that improve wireless communications may bebeneficial.

SUMMARY

A method for wireless communication is described. The method includesreceiving a signal that is pattern-mapped and Gaussian frequency-shiftkeying (GFSK) modulated. The method also includes performing a jointdemapping and demodulation of the received signal based on a storedaccumulated phase.

The method may also include updating the stored accumulated phase basedon the joint demapping and demodulation.

Performing the joint demapping and demodulation of the received signalmay include performing a combined matched filtering and phase rotationof the received signal. The matched filtering may determine the patternmapping of the received signal. The phase rotation of the receivedsignal may be based on the stored accumulated phase.

The stored accumulated phase may be determined from an output of thecombined matched filtering and phase rotation. Performing a combinedmatched filtering and phase rotation of the received signal may includeperforming phase rotation using the stored accumulated phase tocompensate for a phase of the received signal. Matched filtering may beperformed using a resulting phase of the phase rotation to determine anoutput bit.

The phase rotation based on the stored accumulated phase may occurbefore matched filtering. Matched filtering may occur before the phaserotation based on the stored accumulated phase.

The stored accumulated phase may be fed back to perform phase rotationof the received signal. Performing the joint demapping and demodulationof the received signal may also include generating a soft input for aViterbi decoder.

A wireless communication device is also described. The wirelesscommunication device may include a receiver configured to receive asignal that is pattern-mapped and GFSK modulated. The wirelesscommunication device may also include a joint demodulator/demapperconfigured to perform a joint demapping and demodulation of the receivedsignal based on a stored accumulated phase.

An apparatus for wireless communication is also described. The apparatusincludes means for receiving a signal that is pattern-mapped and GFSKmodulated. The apparatus also includes means for performing a jointdemapping and demodulation of the received signal based on a storedaccumulated phase.

A computer-program product for wireless communication is also described.The computer-program product includes a non-transitory tangiblecomputer-readable medium having instructions thereon. The instructionsinclude code for causing a wireless communication device to receive asignal that is pattern-mapped and GFSK modulated. The instructions alsoinclude code for causing the wireless communication device to perform ajoint demapping and demodulation of the received signal based on astored accumulated phase.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating one configuration of a receivingcommunication device in which systems and methods for joint demodulationand demapping may be implemented;

FIG. 2 is a flow diagram illustrating a method for joint demodulationand demapping;

FIG. 3 is a block diagram illustrating one example of components thatmay be implemented for joint demodulation and demapping;

FIG. 4 is a block diagram illustrating one example of components thatmay be included in a joint demodulator/demapper;

FIG. 5 is a block diagram illustrating another example of componentsthat may be included in a joint demodulator/demapper;

FIG. 6 is a block diagram illustrating another more specificconfiguration of a wireless communication device in which systems andmethods for joint demodulation and demapping may be implemented; and

FIG. 7 illustrates certain components that may be included within awireless communication device.

DETAILED DESCRIPTION

The systems and methods disclosed herein may provide receive (Rx)schemes for performing joint demodulation and demapping. The jointdemodulation and demapping described herein may result in betterperformance compared with non-joint approaches to demodulation anddemapping.

The systems and methods described herein may be implemented on a varietyof different electronic devices. Examples of electronic devices includegeneral purpose or special purpose computing system environments orconfigurations, personal computers (PCs), server computers, handheld orlaptop devices, multiprocessor systems, microprocessor-based systems,programmable consumer electronics, network PCs, minicomputers, mainframecomputers, distributed computing environments that include any of theabove systems or devices and the like. The systems and methods may alsobe implemented in mobile devices such as phones, smartphones, wirelessheadsets, personal digital assistants (PDAs), ultra-mobile personalcomputers (UMPCs), mobile Internet devices (MIDs), etc. Further, thesystems and methods may be implemented by battery-operated devices,sensors, etc.

The following description refers to wireless communication devices forclarity and to facilitate explanation. Those of ordinary skill in theart will understand that a wireless communication device may compriseany of the devices described above as well as a multitude of otherdevices.

The Bluetooth wireless communication standard is typically employed forexchanging communications between fixed or mobile Bluetooth-enableddevices over short distances. In some configurations, the systems andmethods disclosed herein may be applied to joint demodulation anddemapping of a received signal by Bluetooth low energy long range (LELR)devices. LELR refers to the “Low Energy Long Range” extension of theBluetooth standard. The LELR extension is focused on energy-constrainedapplications such as battery-operated devices, sensor applications, etc.

The following description uses terminology associated with the Bluetoothand LELR standards. Nevertheless, the concepts are applicable to othertechnologies and standards that involve modulating and transmittingdigital data. Accordingly, while some of the description is provided interms of Bluetooth standards, the systems and methods disclosed hereinmay be implemented more generally in wireless communication devices thatmay not conform to Bluetooth standards.

A Bluetooth LE device may comprise a transmitter, a receiver, or both atransmitter and a receiver. A Bluetooth LE device may also use afrequency-hopping transceiver to combat interference and fading.

One benefit of the systems and methods described herein is that they maybe applied to (e.g., overlaid atop) any existing LE scheme with onlyminimal changes required. In some configurations, the systems andmethods disclosed herein improve the performance of an LE receiver byimplementing joint demodulation/decoding at the receiver.

LE systems operate in the unlicensed 2.4 gigahertz (GHz)Industrial-Scientific-Medical (ISM) band at 2.400-2.4835 GHz(2400-2483.5 megahertz (MHz)). The operating frequency bands of LEsystems are illustrated in Equation (1). In particular, LE systems useforty radio frequency (RF) channels. These RF channels have centerfrequencies (f) of 2402+k*2 MHz, where k=0, . . . , 39.

The detailed description set forth below in connection with the appendeddrawings is intended as a description of exemplary implementations ofthe disclosure and is not intended to represent the only implementationsin which the disclosure may be practiced. The term “exemplary” usedthroughout this description means “serving as an example, instance, orillustration,” and should not necessarily be construed as preferred oradvantageous over other exemplary implementations. The detaileddescription includes specific details for the purpose of providing athorough understanding of the exemplary implementations of thedisclosure. In some instances, some devices are shown in block diagramform.

While for purposes of simplicity of explanation, the methodologies areshown and described as a series of acts, it is to be understood andappreciated that the methodologies are not limited by the order of acts,as some acts may, in accordance with one or more aspects, occur indifferent orders and/or concurrently with other acts from those shownand described herein. For example, those skilled in the art willunderstand and appreciate that a methodology could alternatively berepresented as a series of interrelated states or events, such as in astate diagram. Moreover, not all illustrated acts may be required toimplement a methodology in accordance with one or more aspects.

Various configurations are now described with reference to the Figures,where like reference numbers may indicate functionally similar elements.The systems and methods as generally described and illustrated in theFigures herein could be arranged and designed in a wide variety ofdifferent configurations. Thus, the following more detailed descriptionof several configurations, as represented in the Figures, is notintended to limit scope, as claimed, but is merely representative of thesystems and methods.

FIG. 1 is a block diagram illustrating one configuration of a receivingcommunication device 118 in which systems and methods for jointdemodulation and demapping may be implemented. The receivingcommunication device 118 may be included in a wireless communicationsystem 100 that also includes a transmitting communication device 102.Wireless communication systems 100 are widely deployed to providevarious types of communication content such as voice, data and so on.The transmitting communication device 102 and the receivingcommunication device 118 are examples of wireless communication devices.

Although FIG. 1 depicts a transmitting communication device 102 and areceiving communication device 118, a wireless communication device maybe capable of both transmitting and receiving. Thus, a single wirelesscommunication device may include all of the components depicted in thetransmitting communication device 102 and the receiving communicationdevice 118. In addition, a wireless communication device may includeother components not illustrated in FIG. 1. Those skilled in the artwill understand that the wireless communication devices of FIG. 1 havebeen simplified to facilitate explanation.

Communications in the wireless system may be achieved throughtransmissions over a wireless link. Such a wireless link may beestablished via a single-input and single-output (SISO), multiple-inputand single-output (MISO) or a multiple-input and multiple-output (MIMO)system. A MIMO system includes transmitter(s) and receiver(s) equipped,respectively, with multiple (N_(T)) transmit antennas and multiple(N_(R)) receive antennas for data transmission. In some configurations,the wireless communication system 100 may utilize MIMO. A MIMO systemmay support time division duplex (TDD) and/or frequency division duplex(FDD) systems.

In some configurations, the wireless communication system 100 mayoperate in accordance with one or more standards. Examples of thesestandards include Bluetooth (e.g., Institute of Electrical andElectronics Engineers (IEEE) 802.15.1), IEEE 802.11 (Wi-Fi), IEEE 802.16(Worldwide Interoperability for Microwave Access (WiMAX)), Global Systemfor Mobile Communications (GSM), Universal Mobile TelecommunicationsSystem (UMTS), CDMA2000, Long Term Evolution (LTE), etc. Accordingly,the transmitting communication device 102 may communicate with thereceiving communication device 118 using a communication protocol suchas Bluetooth LE or Bluetooth LELR in some configurations.

In some configurations, the wireless communication system 100 may be amultiple-access system capable of supporting communication with multiplewireless communication devices by sharing the available system resources(e.g., bandwidth and transmit power). Examples of such multiple-accesssystems include code division multiple access (CDMA) systems, widebandcode division multiple access (W-CDMA) systems, time division multipleaccess (TDMA) systems, frequency division multiple access (FDMA)systems, orthogonal frequency division multiple access (OFDMA) systems,evolution-data optimized (EV-DO), single-carrier frequency divisionmultiple access (SC-FDMA) systems, General Packet Radio Service (GPRS)access network systems, 3rd Generation Partnership Project (3GPP) LongTerm Evolution (LTE) systems, and spatial division multiple access(SDMA) systems.

In LTE and UMTS, a wireless communication device may be referred to as a“user equipment” (UE). In 3GPP Global System for Mobile Communications(GSM), a wireless communication device may be referred to as a “mobilestation” (MS). The transmitting communication device 102 and/or thereceiving communication device 118 may be referred to as and/or mayinclude some or all of the functionality of a UE, MS, terminal, anaccess terminal, a subscriber unit, a station, etc. Examples of thetransmitting communication device 102 and/or the receiving communicationdevice 118 include cellular phones, smartphones, wireless headsets,wireless speakers, personal digital assistants (PDAs), wireless devices,electronic automobile consoles, gaming systems, wireless controllers,sensors, wireless modems, handheld devices, laptop computers, SessionInitiation Protocol (SIP) phones, wireless local loop (WLL) stations,etc.

The transmitting communication device 102 and/or the receivingcommunication device 118 may include one or more components asillustrated in FIG. 1. For example, the transmitting communicationdevice 102 may include a pattern mapper 106, a modulator 110, atransmitter 114 and/or one or more antennas 116 a-n. The receivingcommunication device 118 may include one or more antennas 120 a-n, areceiver 122 and/or a joint demodulator/demapper 126.

It should be noted that fewer or more components may be included in thetransmitting communication device 102 and/or the receiving communicationdevice 118. Each of the one or more components may be implemented inhardware or in a combination of hardware and software. For example, thejoint demodulator/demapper 126 may be implemented in hardware (e.g.,circuitry) or in a combination of hardware and software (e.g., processorwith instructions).

Lines and/or arrows in the Figures may indicate a coupling betweencomponents. For example, the joint demodulator/demapper 126 may becoupled to the receiver 122, which may be coupled to the one or moreantennas 120 a-n. As used herein, the term “couple” and variationsthereof may denote a direct connection or an indirect connection. Forexample, the joint demodulator/demapper 126 may be directly connected tothe receiver 122 (without any intervening components) or may beindirectly connected to the receiver 122 (through one or moreintervening components).

The transmitting communication device 102 may obtain a string of bits104. Each of the string of bits 104 may have a binary value (e.g., 1 or0, on or off, etc.). The string of bits 104 may represent data fortransmission. For example, the string of bits 104 may represent payloadand/or control information. Examples of the information that may berepresented by the string of bits 104 may include voice calls, Internettraffic, text messages, error-detecting code, error-correcting code,retransmissions, power control bits, access requests, etc. The string ofbits 104 may originate at the transmitting communication device 102and/or from a remote device. The string of bits 104 may have a rate (R)that may be expressed as bits per second (bps).

Obtaining the string of bits 104 may include generating the string ofbits 104 and/or receiving the string of bits 104. For example, thetransmitting communication device 102 may capture, digitize and/orencode a voice signal to obtain the string of bits 104. In anotherexample, the transmitting communication device 102 may receive textinput from a user, which the transmitting communication device 102 mayformat into the string of bits 104. In yet another example, thetransmitting communication device 102 may receive the string of bits 104from a remote device (via wired or wireless transmission, for example).

The transmitting communication device 102 may provide the string of bits104 to the pattern mapper 106. The pattern mapper 106 may receive thestring of bits 104 that represent data for transmission. The patternmapper 106 may map each bit in the string of bits 104 to a bit patternto create a series 108 of bit patterns. The pattern mapper 106 may mapone input bit into K output bits (i.e., the series 108 of bit patterns).Therefore, the series 108 of bit patterns may be expressed as K*R bps.

In an example, the pattern mapper 106 may create (e.g., generate) a bitpattern for each bit as indicated by each bit (e.g., binary value) inthe string of bits 104. Each bit pattern may be a set of bits with apredetermined pattern of binary values. Each bit pattern (e.g., set ofbits) may have a predetermined size (e.g., length) or include apredetermined number of bits. Mapping each bit in the string of bits 104may include selecting a first bit pattern if a bit has a first binaryvalue (e.g., 0) and selecting a second bit pattern if the bit has asecond binary value (e.g., 1).

The pattern mapper 106 may concatenate the bit patterns selected foreach bit in the string of bits 104 to create the series 108 of bitpatterns. In some configurations, the bit patterns may be concatenatedin the same order as the order of corresponding bits in the string ofbits 104. Alternatively, the number of bit patterns (e.g., sets of bits)in the series 108 may be the same as the number of bits in the string ofbits 104 (when K=1, for instance).

In some configurations, the pattern mapper 106 may perform the mappingwith bit patterns of different sizes and/or in accordance with multiplerates. A pattern mapper 106 that is capable of utilizing bit patterns ofdifferent sizes and/or in accordance with multiple rates may be referredto as a variable-rate pattern mapper.

The pattern mapper 106 may map each bit in the string of bits 104 to abit pattern to create a series 108 of bit patterns before modulation. Ascan be observed, the mapping may change the bit rate (e.g., throughput).The pattern mapper 106 may concatenate the bit patterns in the sameorder as the string of binary bits. The series 108 of concatenated bitpatterns may be provided to the modulator 110.

The modulator 110 may generate a modulated signal 112 based on theseries 108. The modulator 110 may use the series 108 of bit patterns togenerate a series 108 of phase patterns. In some configurations, themodulation performed by the modulator 110 may be constant-envelopemodulation. In other words, generating the modulated signal 112 may bebased on constant-envelope modulation. Constant-envelope modulation(e.g., frequency-shift keying (FSK), Gaussian frequency-shift keying(GFSK), phase-shift keying (PSK), etc.) may be modulation that does notmodulate signal amplitude.

One particular example of constant-envelope modulation is GFSKmodulation. For instance, the modulator 110 may use GFSK modulation togenerate the modulated signal 112 from the series 108 of concatenatedphase patterns. For example, LE or LELR systems may use GaussianFrequency-Shift Keying (GFSK) modulation with a bandwidth bit periodproduct BT=0.5 (where B is bandwidth and T is a bit period). Thisparticular sub-class of GFSK may be referred to as Gaussian MinimumShift Keying (GMSK). The modulation index is between 0.45 and 0.55. Insome configurations, a positive frequency deviation represents binaryone and a negative frequency deviation represents binary zero.

The modulated signal 112 generated by the modulator 110 may be providedto the transmitter 114. In some configurations, the modulated signal 112may include in-phase (I) and quadrature (Q) components (e.g., componentsignals). Accordingly, the modulated signal 112 may be anin-phase/quadrature (IQ) waveform in some examples.

The transmitter 114 may transmit the modulated signal 112 to thereceiving communication device 118. For example, the transmitter 114 mayfilter and/or amplify the modulated signal 112, which may be provided tothe one or more antennas 116 a-n. The one or more antennas 116 a-n mayradiate the modulated signal 112.

The receiver 122 on the receiving communication device 118 may receivethe signal transmitted by the transmitting communication device 102 viaone or more antennas 120 a-n. The receiver 122 may obtain a receivedmodulated signal 124. For example, the receiver 122 may receive (via oneor more antennas 120 a-n), amplify and/or filter the signal receivedfrom the transmitting communication device 102 to produce the receivedmodulated signal 124. The received modulated signal 124 may include Iand Q components (e.g., component signals). Accordingly, the receivedmodulated signal 124 may be an IQ waveform in some examples.

The receiver 122 may provide the received modulated signal 124 to thejoint demodulator/demapper 126. It should be noted that although thereceiver 122 and the joint demodulator/demapper 126 are depicted asseparate components in FIG. 1, in another configuration, the jointdemodulator/demapper 126 may be implemented within the receiver 122.

In a conventional approach, the receiving communication device 118 mayfirst perform demodulation of the received modulated signal 124 (e.g.,the GFSK symbols). The demodulated signal may then be demapped togenerate the received bits 130 (e.g., the information bits). However,improvements may be achieved by performing a joint demodulation anddemapping according to the described systems and methods. For example,the described joint demodulation and demapping may improve the bit errorrate (BER) of the received signal.

The joint demodulator/demapper 126 may obtain the received modulatedsignal 124 (e.g., an IQ waveform). The joint demodulator/demapper 126may determine a string of received bits 130 based on the receivedmodulated signal 124. The joint demodulator/demapper 126 may combinefunctions of a demodulator (e.g., GFSK demodulator) and a patterndemapper.

The joint demodulator/demapper 126 may determine the string of receivedbits 130 based on bit patterns (and based on phase patterns thatcorrespond to the bit patterns, for example) of the received modulatedsignal 124 and based on a stored accumulated phase 128. For instance,the joint demodulator/demapper 126 may utilize matched filtering todetermine the pattern mapping. The joint demodulator/demapper 126 mayalso perform phase rotation of the received signal 124 based on thestored accumulated phase 128.

In some configurations, the joint demodulator/demapper 126 maydemodulate and demap pattern-mapped and GFSK modulated signals 124 inthe IQ domain. For example, the joint demodulator/demapper 126 mayperform one or more of the following procedures in order to determinethe string of received bits 130. In an implementation, the jointdemodulator/demapper 126 may use the stored accumulated phase 128 in adecision feedback loop to reconstruct the initial phase at the beginningof a pattern. A matched filter in the IQ domain may be used to continuethe demodulation process.

The joint demodulator/demapper 126 may perform a combined phase rotationand matched filtering. The phase rotation may compensate for the phaseof the received modulated signal 124. The phase rotation may beperformed using a stored accumulated phase 128. The jointdemodulator/demapper 126 may perform matched filtering using theresulting phase to determine the pattern mapping of the receivedmodulated signal 124.

Upon performing the combined phase rotation and matched filtering, thejoint demodulator/demapper 126 may output the received bits 130. Thejoint demodulator/demapper 126 may then update the stored accumulatedphase 128 based on the joint demapping and demodulation output. In aconfiguration, the stored accumulated phase 128 may be stored in memory.Therefore, the memory may store the up-to-date accumulated phase of thereceived modulated signal 124.

The joint demodulator/demapper 126 may determine the phase 128 from theoutput of the combined matched filtering and phase rotation. The jointdemodulator/demapper 126 may then update the stored accumulated phase128. The stored accumulated phase 128 may be fed back to perform asubsequent phase rotation of the received signal 124. Further details onperforming a joint demapping and demodulation of the received signalbased on the stored accumulated phase 128 are described in connectionwith FIG. 3.

It should be noted that switching the order of the phase rotation andthe matched filtering may result in alternative implementations. In oneimplementation, matched filtering occurs before the phase rotation asdescribed in connection with FIG. 4. In another implementation, thephase rotation based on the stored accumulated phase 128 occurs beforematched filtering as described in connection with FIG. 5.

In an implementation, the received bits 130 may be provided to a decoder(not shown) for decoding. For example, the received bits 130 generatedby the joint demodulator/demapper 126 may be soft input for a Viterbidecoder.

FIG. 2 is a flow diagram illustrating a method 200 for jointdemodulation and demapping. The method 200 may be performed by areceiving communication device 118. The receiving communication device118 may receive 202 a signal 124 that is pattern-mapped and GFSKmodulated. This may be accomplished as described above in connectionwith FIG. 1. For example, the receiving communication device 118 mayreceive (via one or more antennas 120 a-n), amplify and/or filter asignal to produce the received modulated signal 124.

The receiving communication device 118 may perform 204 a joint demappingand demodulation of the received signal 124 based on a storedaccumulated phase 128. This may be accomplished as described above inconnection with FIG. 1. For example, the receiving communication device118 may perform a combined phase rotation and matched filtering. Thephase rotation may compensate for the phase of the received modulatedsignal 124. The phase rotation may be performed using the storedaccumulated phase 128. The receiving communication device 118 mayperform matched filtering using the resulting phase to determine thepattern mapping of the received modulated signal 124. Upon performingthe combined phase rotation and matched filtering, the receivingcommunication device 118 may output the received bits 130.

The receiving communication device 118 may update 206 the storedaccumulated phase 128 based on the joint demapping and demodulationoutput. This may be performed as described above in connection withFIG. 1. For example, the receiving communication device 118 may storethe stored accumulated phase 128 in memory. The receiving communicationdevice 118 may update the memory with the up-to-date accumulated phaseof the received modulated signal 124.

FIG. 3 is a block diagram illustrating one example of components thatmay be implemented for joint demodulation and demapping. In particular,FIG. 3 illustrates a joint demodulator/demapper 326 that includes acombined matched filtering and phase rotation block 332 and anaccumulated phase determination block 334. One or more of theseillustrated components may be included in the receiving communicationdevice 118 described in connection with FIG. 1 in some configurations.For example, one or more of the illustrated components may be includedin the receiver 122, in the joint demodulator/demapper 126 or both insome configurations.

One or more of the functions or procedures described in connection withFIG. 3 may be performed as part of joint demodulation and demapping. Asdescribed above, for example, the joint demodulator/demapper 326 maytake LE modulated IQ values as input and may perform a jointdemodulation/decoding operation to convert the IQ values to receiveddata. For instance, the joint demodulator/demapper 326 may perform acombined matched filtering and phase rotation of the received GFSKmodulated signal 324 (based on the stored accumulated phase 328) todetermine a string of received bits 330 (e.g., a string of binary dataincluding is and/or Os).

In an implementation, the joint demodulation and demapping may includemulti-symbol decision feedback demodulation. The baseband model of theGFSK modulated signal 324 is given by

$\begin{matrix}{{s(t)} = {\sqrt{\frac{E_{S}}{T}}{{\mathbb{e}}^{{j\phi}{({t,I})}}.}}} & (1)\end{matrix}$

In Equation (1), E_(S) is the symbol energy, T is the symbol duration,and φ(t,I) is the data dependent time-varying modulated phase with theinformation bit sequence I. The phase φ(t,I) is given by

$\begin{matrix}\begin{matrix}{{{\phi\left( {t,I} \right)} = {2\pi\; h{\sum\limits_{k = 0}^{{N\; Q} - 1}{{I\lbrack k\rbrack}{q\left( {t - {k\; T}} \right)}}}}},} \\{{= {{\pi\; h{\sum\limits_{k = 0}^{n - L}{I\lbrack k\rbrack}}} + {2\pi{\sum\limits_{k = {n - L + 1}}^{n}{{I\lbrack k\rbrack}{q\left( {t - {k\; T}} \right)}}}}}},} \\{{{n\; T} \leq t \leq {\left( {n + 1} \right)T}},}\end{matrix} & (2)\end{matrix}$where I[k] is the k-th symbol, N is the total number of bits per packetand Q is the number of symbols representing a bit, thus NQ is the totalnumber of symbols per packets, h is the modulation index, q(t)=∫₀^(t)g(τ)dτ, where g(t) is the Gaussian filter, which is the impulseresponse of the convolution of a Gaussian distribution and a rectangularpulse of period T, and L is the length of g(t) in terms of the symbolduration.

The Gaussian filter g(t) can be given by

$\begin{matrix}{{{g(t)} = {\frac{1}{2\; T}\left\lbrack {{Q\left( {2\pi\; B\frac{t - {\left( {L + 1} \right)\frac{T}{2}}}{\sqrt{\log\; 2}}} \right)} - {Q\left( {2\;\pi\; B\frac{1 - {\left( {L - 1} \right)\frac{T}{2}}}{\sqrt{\log\; 2}}} \right)}} \right\rbrack}},} & (3)\end{matrix}$where Q(·) is the Q-function, and B is a 3 dB bandwidth of the Gaussianfilter.

The received GFSK modulated signal 324 is given byr(t)=s(t)e ^(jφ) ⁰ +z(t),  (4)where φ₀ is the unknown initial phase and z(t) is the additive whiteGaussian noise.

Sampling the received GFSK modulated signal 324 at symbol rate,r(nT)=s(nT)e ^(jφ) ⁰ +z(nT),  (5)r[n]=s[n]e ^(jφ) ⁰ +z[n],  (6)where r[n], s[n], z[n] denote the discrete samples. In animplementation, BT=0.5, L=3 is sufficient for modeling the ISI effect.Then, s[n] can be expressed as

$\begin{matrix}{{{{s\lbrack n\rbrack} = {\sqrt{\frac{E_{S}}{T}}{\mathbb{e}}^{{j\phi}{\lbrack n\rbrack}}}},{with}}\begin{matrix}{{{\phi\lbrack n\rbrack} = {{\pi\; h{\sum\limits_{k = 0}^{n - 2}{I\lbrack k\rbrack}}} + {2\pi\; h\;{q(T)}\left( {{I\left\lbrack {n - 1} \right\rbrack} - {I\left\lbrack {n - 2} \right\rbrack}} \right)}}},} \\{{= {{\phi_{S}\lbrack n\rbrack} + {\phi_{E}\lbrack n\rbrack}}},}\end{matrix}} & (7)\end{matrix}$where, for n≧2,

$\begin{matrix}{{{\phi_{S}\lbrack n\rbrack} = {\pi\; h{\sum\limits_{k = 0}^{n - 2}{I\lbrack k\rbrack}}}},} & (8)\end{matrix}$

$\begin{matrix}{{\phi_{E}\lbrack n\rbrack} = \left\{ \begin{matrix}{0,} & {{{{I\left\lbrack {n - 1} \right\rbrack}{I\left\lbrack {n - 2} \right\rbrack}} = 1},} \\{{4\;\pi\; h\;{q(T)}},} & {{{I\left\lbrack {n - 1} \right\rbrack} = 1},{{I\left\lbrack {n - 2} \right\rbrack} = {- 1}},} \\{{{- 4}\;\pi\; h\;{q(T)}},} & {{{I\left\lbrack {n - 2} \right\rbrack} = {- 1}},{{I\left\lbrack {n - 2} \right\rbrack} = {- 1}},}\end{matrix} \right.} & (9)\end{matrix}$with φ_(S)[0]=φ_(S)[1]=0, φ_(E)[0]=0, and φ_(E)[1]=2πhq(T)I[0].

It can be seen that φ_(S)[n] denotes the accumulated phase 328 of thefirst (n−1) symbols, and φ_(E)[n] denotes the ISI effect to the (n−2)-thsymbol caused by the (n−1)-th symbol.

In the following description, the maximum likelihood estimation of theinitial phase φ₀ is described. A demodulation approach is discussedgiven such an estimation.

The maximum likelihood estimation of an information bit and the initialphase may be given by

$\begin{matrix}{{{ML}\text{:}{\max\limits_{\phi_{0},I}{\Pr\left( {\left. r \middle| s \right.,\phi_{0}} \right)}}},\left. \Rightarrow{\max\limits_{\phi_{0},I}{\exp\left\{ {{- \frac{1}{2\;\sigma^{2}}}{{r - {s\;{\mathbb{e}}^{{j\phi}_{0}}}}}^{2}} \right\}}} \right.,\left. \Rightarrow{\max\limits_{\phi_{0},I}{{r - {s\;{\mathbb{e}}^{{j\phi}_{0}}}}}^{2}} \right.,\left. \Rightarrow{\max\limits_{\phi_{0},I}{{Re}\left\lbrack {s^{H}r\;{\mathbb{e}}^{- {j\phi}_{0}}} \right\rbrack}} \right.,} & (10)\end{matrix}$where r is the vector of the received signal samples, [r[0], r[1], . . ., r[mQ+1]]^(T), s is the vector of the transmitted signal samples,[s[0], s[1], . . . s[mQ+1]]^(T), which is a function of the informationbits I, σ² is the noise variance, and (·)^(H) is the Hermitian operator.

It should be noted that from Equation (8), there is a 2 sample delay fordecoding. In other words, r[n+2] should be used to decode I[n]. It canbe seen that

$\begin{matrix}{{\max\limits_{\phi_{0},I}{{Re}\left\lbrack {s^{H}r\;{\mathbb{e}}^{- {j\phi}_{0}}} \right\rbrack}},{= {\max\limits_{I}{{s^{H}r}\; }}},} & (11)\end{matrix}$and the optimum maximizer {circumflex over (φ)}₀ satisfies

$\begin{matrix}{{\mathbb{e}}^{j{\hat{\phi}}_{0}} = {\frac{s^{H}r}{{s^{H}r}}.}} & (12)\end{matrix}$

Expanding the metric in Equation (11), results in

$\begin{matrix}\begin{matrix}{{{s^{H}r}} = {{{\sum\limits_{n = 0}^{{mQ} + 1}{{r\lbrack n\rbrack}s*\lbrack n\rbrack}}} = {{\sum\limits_{n = 0}^{{mQ} + 1}{{r\lbrack n\rbrack}{\mathbb{e}}^{- {{j\phi}{\lbrack n\rbrack}}}}}}}} \\{= {{{\sum\limits_{n = 0}^{{{({m - 1})}Q} + 1}{{r\lbrack n\rbrack}{\mathbb{e}}^{- {{j\phi}{\lbrack n\rbrack}}}}} + {\sum\limits_{n = {{{({m - 1})}Q} + 2}}^{{mQ} + 1}{{r\lbrack n\rbrack}{\mathbb{e}}^{- {{j\phi}{\lbrack n\rbrack}}}}}}}} \\{= {{{\mathbb{e}}^{- {{j\phi}_{S}{\lbrack{{{({m - 1})}Q} + 1}\rbrack}}} \cdot}}} \\{\left( {{\sum\limits_{n = 0}^{{{({m - 1})}Q} + 1}{{r\lbrack n\rbrack}{\mathbb{e}}^{- {j{({{\phi_{S}{\lbrack n\rbrack}} - {\phi_{S}{\lbrack{{{({m - 1})}Q} + 1}\rbrack}}})}}}{\mathbb{e}}^{- {{j\phi}_{E}{\lbrack n\rbrack}}}}} +} \right.} \\{\left. {\sum\limits_{n = {{{({m - 1})}Q} + 2}}^{{mQ} + 1}{{r\lbrack n\rbrack}{\mathbb{e}}^{- {j{({{\phi_{S}{\lbrack n\rbrack}} - {\phi_{S}{\lbrack{{{({m - 1})}Q} + 1}\rbrack}}})}}}{\mathbb{e}}^{- {{j\phi}_{E}{\lbrack n\rbrack}}}}} \right)} \\{= {{{\sum\limits_{n = 0}^{{{({m - 1})}Q} + 1}{{r\lbrack n\rbrack}{\mathbb{e}}^{- {j{({{\phi_{S}{\lbrack n\rbrack}} - {\phi_{S}{\lbrack{{{({m - 1})}Q} + 1}\rbrack}}})}}}{\mathbb{e}}^{- {{j\phi}_{E}{\lbrack n\rbrack}}}}} +}}} \\{{\sum\limits_{n = {{{({m - 1})}Q} + 2}}^{{mQ} + 1}{{r\lbrack n\rbrack}{\mathbb{e}}^{- {j{({{\phi_{S}{\lbrack n\rbrack}} - {\phi_{S}{\lbrack{{{({m - 1})}Q} + 1}\rbrack}}})}}}{\mathbb{e}}^{- {{j\phi}_{E}{\lbrack n\rbrack}}}}}} \\{= {{{{M_{Q}\left\lbrack {m - 1} \right\rbrack} + {s_{Q}^{H}{r_{Q}\lbrack m\rbrack}}}}.}}\end{matrix} & (13)\end{matrix}$

In Equation (13), m denotes the m-th information bit associating withthe Q symbols, which correspond to the received samples r[(m−1)Q+2], . .. , r[mQ+1]. The notation M_(Q)[m−1] is defined as

$\begin{matrix}{{M_{Q}\left\lbrack {m - 1} \right\rbrack} = {\sum\limits_{n = 0}^{{{({m - 1})}Q} + 1}{{r\lbrack n\rbrack}{\mathbb{e}}^{- {j{({{\phi_{S}{\lbrack n\rbrack}} - {\phi_{S}{\lbrack{{{({m - 1})}Q} + 1}\rbrack}}})}}}{{\mathbb{e}}^{- {{j\phi}_{E}{\lbrack n\rbrack}}}.}}}} & (14)\end{matrix}$

The updating rule of M_(Q)[m] given M_(Q)[m−1] can be derived asM _(Q) [m]=(M _(Q) [m−1]+s _(Q) ^(H) r _(Q) [m])e ^(j(φ) ^(S)^([mQ+1]−φ) ^(S) ^([(m−1)Q+1])).  (15)

In Equation (15), r_(Q)[m] and s_(Q) are vectors defined as

$\begin{matrix}{{{r_{Q}\lbrack m\rbrack} = \begin{bmatrix}{r\left\lbrack {{\left( {m - 1} \right)Q} + 2} \right\rbrack} \\{r\left\lbrack {{\left( {m - 1} \right)Q} + 3} \right\rbrack} \\\vdots \\{r\left\lbrack {{mQ} + 1} \right\rbrack}\end{bmatrix}},{s_{Q} = {\begin{bmatrix}{{\mathbb{e}}^{j{({{\phi_{S}{\lbrack{{{({m - 1})}Q} + 2}\rbrack}} - {\phi_{S}{\lbrack{{{({m - 1})}Q} + 1}\rbrack}}})}}{\mathbb{e}}^{{j\phi}_{E}{\lbrack{{{({m - 1})}Q} + 2}\rbrack}}} \\{{\mathbb{e}}^{j{({{\phi_{S}{\lbrack{{{({m - 1})}Q} + 3}\rbrack}} - {\phi_{S}{\lbrack{{{({m - 1})}Q} + 1}\rbrack}}})}}{\mathbb{e}}^{{j\phi}_{E}{\lbrack{{{({m - 1})}Q} + 3}\rbrack}}} \\\vdots \\{{\mathbb{e}}^{j{({{\phi_{S}{\lbrack{{mQ} + 1}\rbrack}} - {\phi_{S}{\lbrack{{{({m - 1})}Q} + 1}\rbrack}}})}}{\mathbb{e}}^{{j\phi}_{E}{\lbrack{{mQ} + 1}\rbrack}}}\end{bmatrix}.}}} & (16)\end{matrix}$

Thus, the ML detection in Equation (11) can be written as

$\begin{matrix}\left. {\max\limits_{I}{{s^{H}r}}}\Rightarrow{\max\limits_{I}{{{{M_{Q}\left\lbrack {m - 1} \right\rbrack} + {s_{Q}^{H}{r_{Q}\lbrack m\rbrack}}}}.}} \right. & (17)\end{matrix}$

The symbols I[mQ], I[mQ+1], . . . , I[mQ+Q−1] associated with the m-thinformation bit B[m] may be denoted as I_(m). Considering a decisionfeedback scenario, the information bits B[0], . . . , B[m−1] have beendemodulated. The maximization in Equation (17) may be expressed as

$\begin{matrix}{{\max\limits_{I_{m}}{{Re}\left\lbrack {{M_{Q}^{*}\left\lbrack {m - 1} \right\rbrack}s_{Q}^{H}{r_{Q}\lbrack m\rbrack}} \right\rbrack}},} & (18)\end{matrix}$since M_(Q)[m−1] contains only I₀, . . . , I_(m-1). Iteratively applyingthe updating rule of Equation (15) and the maximization of Equation(18), the decision feedback demodulation algorithm may be according toTable 1.

TABLE 1 Multi-Symbol GFSK Demodulation Algorithm  (i) Initial phaseestimation using training sequence {I_(tr)[m]}_(m=0) ^(N) ^(tr−1) : 1.Initialize M_(tr)[0] = r_(tr)[0] + r_(tr)[1]e^(−jφ) ^(E) ^([1]). 2. Form = 0 to N_(tr) − 1   M_(tr)[m + 1] = wM_(tr)[m]e^(jπhI) ^(tr) ^([m]) +r_(tr)[m + 2]e^(−jφ) ^(E) ^([m+2]). end (ii) Phase tracking andmulti-symbol detection: 1. Initialize M_(Q)[0] = M_(tr)[N_(tr)]. 2. Form = 0 to N_(B) − 1   {circumflex over (B)}[m] = î = arg max_(i)Re{M_(Q)*[m](S_(Q) ^((i)))^(H) r_(Q)[m + 1]}   M_(Q)[m + 1] =(M_(Q)[m] + (s_(Q) ^((i)))^(H) r_(Q)[m + 1]) ·        e^(j(φ) ^(S)^([(m+1)Q+1]−φ) ^(S) ^([mQ+1])) end

It should be noted that in Table (1), s_(Q) ^((i)) denotes the matchedfilter corresponding to the i-th hypothesis, r_(Q) denotes the output ofthe phase rotation and M_(Q)[m+1] corresponds to the updated storedaccumulated phase 328 (which may be performed by the accumulated phasedetermination block 334. {circumflex over (B)}[m] corresponds to thereceived bits 330 that are output by the combined matched filtering andphase rotation block 332.

For the maximum likelihood (ML) estimation of the initial phase, usingEquation (12) and Equation (13), the ML estimation of φ₀ may be derivedto bee ^(j{circumflex over (φ)}) ⁰ =e ^(−jφ) ^(S) ^([(m−1)Q+1])(M _(Q)[m−1]+s _(Q) ^(H) r _(Q) [m]).  (19)

Comparing Equation (15) and Equation (19),M _(Q) [m]=e ^(j{circumflex over (φ)}) ⁰ e ^(jφ) ^(S) ^([mQ+1]),  (20)which means the phase accumulated up to the (mQ+1)-th sample. With thisthe phase of the next Q samples may be compensated for demodulating thenext bit. In other words, if the estimated initial phase is accurateenough, the resulting performance may approach a coherent demodulation.

For Q=1, Equation (15) becomesM ₁ [m]=M ₁ [m−1]e ^(jπhI[m−1]) +r[m+1]e ^(jφ) ^(E) ^([m+1]).  (21)

The result of Equation (21) may be useful for training the initial phasebefore symbol estimation if a training sequence is available.

As indicated by the algorithm of Table (1), given the initial phaseestimate {circumflex over (φ)}₀, the ML demodulation can be determinedby first compensating the phase of the received samples, which are thencorrelated with the matched sequences of each hypothesis. That is,

$\begin{matrix}{{\hat{i} = {\arg\;{\max\limits_{i}{{Re}\left\{ {{M_{Q}^{*}\left\lbrack {m - 1} \right\rbrack}\left( s_{Q}^{(i)} \right)^{H}r_{Q{\lbrack m\rbrack}}} \right\}}}}},} & (22)\end{matrix}$where s_(Q) ^((i)) denotes the matched filter corresponding to the i-thhypothesis.

For interpreting M_(Q)[·], the true symbols may be denoted as I[k], andthe estimated symbols may be denoted as Î[k]. The notations {circumflexover (φ)}_(m)[n−2], {circumflex over (φ)}_(e)[n−1] are accordinglydefined by the estimated symbols. Then,

$\begin{matrix}{{{M\left\lbrack {P - 2} \right\rbrack} = {\sum\limits_{n = 1}^{P}{{\hat{r}\lbrack n\rbrack}{\mathbb{e}}^{j{({{{\hat{\phi}}_{m}{\lbrack{P - 2}\rbrack}} - {{\hat{\phi}}_{m}{\lbrack{n - 2}\rbrack}}})}}}}},} & (23)\end{matrix}$where

$\begin{matrix}\begin{matrix}{{\hat{r}\lbrack n\rbrack} = {{r\lbrack n\rbrack}{\mathbb{e}}^{{- j}{{\hat{\phi}}_{e}{\lbrack{n - 1}\rbrack}}}}} \\{= {\left( {\mathbb{e}}^{{j{({{\phi_{m}{\lbrack{n - 2}\rbrack}} + {\phi_{e}{\lbrack{n - 1}\rbrack}} + \phi_{0}})}} + {z{\lbrack n\rbrack}}} \right){{\mathbb{e}}^{{- j}{{\hat{\phi}}_{e}{\lbrack{n - 1}\rbrack}}}.}}}\end{matrix} & (24)\end{matrix}$

Therefore, M[P−2] can be expressed as

$\begin{matrix}{{{M\left\lbrack {P - 2} \right\rbrack} = {{{\mathbb{e}}^{{j\phi}_{0}}{{\mathbb{e}}^{j{{\hat{\phi}}_{m}{\lbrack{P - 2}\rbrack}}} \cdot {\sum\limits_{n = 1}^{P}{{\mathbb{e}}^{j{({{\phi_{m}{\lbrack{P - 2}\rbrack}} - {{\hat{\phi}}_{m}{\lbrack{n - 2}\rbrack}}})}}{\mathbb{e}}^{j{({{\phi_{e}{\lbrack{n - 1}\rbrack}} - {{\hat{\phi}}_{e}{\lbrack{n - 1}\rbrack}}})}}}}}} + {\overset{\sim}{z}\left\lbrack {P - 2} \right\rbrack}}},} & (25)\end{matrix}$where {tilde over (z)}[P−2]=Σ_(n=1) ^(P)z[n]e^(−jφ) ^(e)^([n−1])e^(j({circumflex over (φ)}) ^(m) ^([P−2]−{circumflex over (φ)})^(m) ^([n−2])). It should be noted that when the SNR is large and if theestimation is mostly correct, then M[P−2] is approximately the initialphase e^(jφ) ⁰ times a constant Pe^(jφ) ^(m[P−2]) , which is theaccumulated phase 328 up to the (P−2)-th symbol.

From Equation (25), when the index P increases, the variance of theequivalent noise {tilde over (z)}[P−2] becomes Pσ_(z) ², where σ_(z) ²is the variance of z[n], while the amplitude of M[P−2] becomes P. Thus,equivalently, the estimation error of e^(jφ) ⁰ is decreasing as Pincreases. The growth of the amplitude of M[P−2] with P also justifiesthe need of a forgetting factor.

In a special case, when the information bits B[m] are encoded by theManchester pattern, the algorithm in Table (1) can be furthersimplified. For the following Manchester encoding with spreading factorQ=4, the encoded symbols are given by

$\begin{matrix}{{I\left\lbrack {4{m:{{4m} + 3}}} \right\rbrack} = \left\{ {\begin{matrix}{1,} & {1,} & {{- 1},} & {{- 1},} & {{{for}\mspace{14mu}{B\lbrack m\rbrack}} = 0} \\{{- 1},} & {{- 1},} & {1,} & {1,} & {{{for}\mspace{14mu}{B\lbrack m\rbrack}} = 1}\end{matrix}.} \right.} & (26)\end{matrix}$

It can be shown that the hypotheses s_(Q) ⁽⁰⁾ and s_(Q) ⁽¹⁾ are complexconjugate to each other. In other words,s _(Q) ⁽⁰⁾ =s _(Q) ⁽¹⁾*.  (27)

Therefore,

$\begin{matrix}{{{\left( s_{Q}^{(0)} \right)^{H}{r_{Q}\left\lbrack {m + 1} \right\rbrack}} = {y_{1} - {jy}_{2}}},} & (28)\end{matrix}$

$\begin{matrix}{{{\left( s_{Q}^{(1)} \right)^{H}{r_{Q}\left\lbrack {m + 1} \right\rbrack}} = {y_{1} + {jy}_{2}}},} & (29)\end{matrix}$

where

y₁ = (Re[s_(Q)⁽⁰⁾])^(H)r_(Q)[m + 1]and

y₂ = (Im[s_(Q)⁽⁰⁾])^(H)r_(Q)[m + 1].The ML detection

$\begin{matrix}{{{Re}\left\lbrack {{M_{Q}^{*}\left( s_{Q}^{(0)} \right)}^{H}{r_{Q}\left\lbrack {m + 1} \right\rbrack}} \right\rbrack}\underset{1}{\overset{0}{\gtrless}}{{Re}\left\lbrack {{M^{*}\left( s_{Q}^{(1)} \right)}^{H}{r_{Q}\left\lbrack {m + 1} \right\rbrack}} \right\rbrack}} & (30)\end{matrix}$becomes

$\begin{matrix}{{{Im}\left\lbrack {M_{Q}^{*}y_{2}} \right\rbrack}\underset{1}{\overset{0}{\lessgtr}}0.} & (31)\end{matrix}$

It should be noted that for both hypotheses, the summation of thesymbols in each symbol sequence is zero. Thus, the accumulated phaseφ_(S)[mQ+1]−φ_(S)[m−1)Q+1]=0 for all m. The Manchester GFSK DemodulationAlgorithm is summarized in Table (2).

TABLE 2 Manchester GFSK Demodulation Algorithm 1. Initialize M_(Q) (bytraining sequence or previous received signal r[1]). 2. For m = 0 toN_(B) − 1 y₁ = (Re[s_(Q) ⁽⁰⁾])^(H) r_(Q)[m + 1] y₂ = (Im[s_(Q) ⁽⁰⁾])^(H)r_(Q)[m + 1] if Im[M_(Q)*y₂] > 0   B[m] = 0   M_(Q) = M_(Q) + y₁ − jy₂else   B[m] = 1   M_(Q) = M_(Q) + y₁ + jy₂ end if end for

FIG. 4 is a block diagram illustrating one example of components thatmay be included in a joint demodulator/demapper 426. The jointdemodulator/demapper 426 includes a matched filter 436, a phase rotator438 and an accumulated phase determination block 434. In theimplementation depicted in FIG. 4, matched filtering occurs before thephase rotation based on the stored accumulated phase 428.

The matched filter 436 may receive the received GFSK modulated signal424. The matched filter 436 may perform matched filtering to determinethe pattern mapping of the received GFSK modulated signal 424. This maybe accomplished as described in connection with FIG. 3. The matchedfilter 436 may output a demapped signal 440.

The phase rotator 438 may receive the demapped signal 440. The phaserotator 438 may also receive a stored accumulated phase 428. The phaserotator 438 may perform phase rotation on the demapped signal 440 basedon the stored accumulated phase 428. This may be accomplished asdescribed in connection with FIG. 3. At this point, the received GFSKmodulated signal 424 is demodulated and demapped. The phase rotator 438may output received bits 430.

The accumulated phase determination block 434 may update the storedaccumulated phase 428 based on the joint demapping and demodulation.This may be accomplished as described in connection with FIG. 3. Itshould be noted that the stored accumulated phase 428 may be stored inmemory. In an implementation, the accumulated phase determination block434 may update the memory upon determining the accumulated phase 428.

FIG. 5 is a block diagram illustrating another example of componentsthat may be included in a joint demodulator/demapper 526. The jointdemodulator/demapper 526 includes a matched filter 536, a phase rotator538 and an accumulated phase determination block 534. In theimplementation depicted in FIG. 5, phase rotation based on the storedaccumulated phase 528 occurs before matched filtering.

The phase rotator 538 may receive the received GFSK modulated signal524. The phase rotator 538 may also receive a stored accumulated phase528. The phase rotator 538 may perform phase rotation on the receivedGFSK modulated signal 524 based on the stored accumulated phase 528.This may be accomplished as described in connection with FIG. 3. Thephase rotator 538 may output a demodulated signal 542.

The matched filter 536 may receive the demodulated signal 542. Thematched filter 536 may perform matched filtering to determine thepattern mapping of the demodulated signal 542. This may be accomplishedas described in connection with FIG. 3. At this point, the received GFSKmodulated signal 524 is demodulated and demapped. The matched filter 536may output received bits 530.

The accumulated phase determination block 534 may update the storedaccumulated phase 528 based on the joint demapping and demodulation.This may be accomplished as described in connection with FIG. 3.

FIG. 6 is a block diagram illustrating another more specificconfiguration of a wireless communication device 649 in which systemsand methods for joint demodulation and demapping may be implemented. Thewireless communication device 649 illustrated in FIG. 6 may be anexample of one or more of the transmitting communication device 102 andthe receiving communication device 118 described in connection with oneor more of FIGS. 1-5. The wireless communication device 649 may includean application processor 621. The application processor 621 generallyprocesses instructions (e.g., runs programs) to perform functions on thewireless communication device 649. The application processor 621 may becoupled to an audio coder/decoder (codec) 619.

The audio codec 619 may be used for coding and/or decoding audiosignals. The audio codec 619 may be coupled to at least one speaker 611,an earpiece 613, an output jack 615 and/or at least one microphone 617.The speakers 611 may include one or more electro-acoustic transducersthat convert electrical or electronic signals into acoustic signals. Forexample, the speakers 611 may be used to play music or output aspeakerphone conversation, etc. The earpiece 613 may be another speakeror electro-acoustic transducer that can be used to output acousticsignals (e.g., speech signals) to a user. For example, the earpiece 613may be used such that only a user may reliably hear the acoustic signal.The output jack 615 may be used for coupling other devices to thewireless communication device 649 for outputting audio, such asheadphones. The speakers 611, earpiece 613 and/or output jack 615 maygenerally be used for outputting an audio signal from the audio codec619. The at least one microphone 617 may be an acousto-electrictransducer that converts an acoustic signal (such as a user's voice)into electrical or electronic signals that are provided to the audiocodec 619.

The application processor 621 may also be coupled to a power managementcircuit 694. One example of a power management circuit 694 is a powermanagement integrated circuit (PMIC), which may be used to manage theelectrical power consumption of the wireless communication device 649.The power management circuit 694 may be coupled to a battery 696. Thebattery 696 may generally provide electrical power to the wirelesscommunication device 649. For example, the battery 696 and/or the powermanagement circuit 694 may be coupled to at least one of the elementsincluded in the wireless communication device 649.

The application processor 621 may be coupled to at least one inputdevice 698 for receiving input. Examples of input devices 698 includeinfrared sensors, image sensors, accelerometers, touch sensors, keypads,etc. The input devices 698 may allow user interaction with the wirelesscommunication device 649. The application processor 621 may also becoupled to one or more output devices 601. Examples of output devices601 include printers, projectors, screens, haptic devices, etc. Theoutput devices 601 may allow the wireless communication device 649 toproduce output that may be experienced by a user.

The application processor 621 may be coupled to application memory 603.The application memory 603 may be any electronic device that is capableof storing electronic information. Examples of application memory 603include double data rate synchronous dynamic random access memory (DDRSDRAM), synchronous dynamic random access memory (SDRAM), flash memory,etc. The application memory 603 may provide storage for the applicationprocessor 621. For instance, the application memory 603 may store dataand/or instructions for the functioning of programs that are run on theapplication processor 621.

The application processor 621 may be coupled to a display controller605, which in turn may be coupled to a display 607. The displaycontroller 605 may be a hardware block that is used to generate imageson the display 607. For example, the display controller 605 maytranslate instructions and/or data from the application processor 621into images that can be presented on the display 607. Examples of thedisplay 607 include liquid crystal display (LCD) panels, light emittingdiode (LED) panels, cathode ray tube (CRT) displays, plasma displays,etc.

The application processor 621 may be coupled to a baseband processor623. The baseband processor 623 generally processes communicationsignals. For example, the baseband processor 623 may demodulate and/ordecode received signals. Additionally or alternatively, the basebandprocessor 623 may encode and/or modulate signals in preparation fortransmission.

The baseband processor 623 may include a joint demodulator/demapper 626.The joint demodulator/demapper 626 may be an example of one or more ofthe joint demodulators/demappers 126, 326, 426, 526 described above. Thejoint demodulator/demapper 626 may perform a joint demapping anddemodulation of a received signal based on a stored accumulated phase628.

The baseband processor 623 may be coupled to baseband memory 609. Thebaseband memory 609 may be any electronic device capable of storingelectronic information, such as SDRAM, DDRAM, flash memory, etc. Thebaseband processor 623 may read information (e.g., instructions and/ordata) from and/or write information to the baseband memory 609.Additionally or alternatively, the baseband processor 623 may useinstructions and/or data stored in the baseband memory 609 to performcommunication operations.

The baseband processor 623 may be coupled to a radio frequency (RF)transceiver 625. The RF transceiver 625 may be coupled to a poweramplifier 627 and one or more antennas 629. The RF transceiver 625 maytransmit and/or receive radio frequency signals. For example, the RFtransceiver 625 may transmit an RF signal using a power amplifier 627and at least one antenna 629. The RF transceiver 625 may also receive RFsignals using the one or more antennas 629.

FIG. 7 illustrates certain components that may be included within awireless communication device 749. The wireless communication device 749described in connection with FIG. 7 may be an example of and/or may beimplemented in accordance with one or more of the transmittingcommunication device 102, the receiving communication device 118 and thewireless communication device 649 described in connection with one ormore of FIGS. 1-6.

The wireless communication device 749 includes a processor 747. Theprocessor 747 may be a general purpose single- or multi-chipmicroprocessor (e.g., an ARM), a special purpose microprocessor (e.g., adigital signal processor (DSP)), a microcontroller, a programmable gatearray, etc. The processor 747 may be referred to as a central processingunit (CPU). Although just a single processor 747 is shown in thewireless communication device 749 of FIG. 7, in an alternativeconfiguration, a combination of processors (e.g., an ARM and DSP) couldbe used.

The wireless communication device 749 also includes memory 731 inelectronic communication with the processor 747 (i.e., the processor 747can read information from and/or write information to the memory 731).The memory 731 may be any electronic component capable of storingelectronic information. The memory 731 may be random access memory(RAM), read-only memory (ROM), magnetic disk storage media, opticalstorage media, flash memory devices in RAM, on-board memory includedwith the processor, programmable read-only memory (PROM), erasableprogrammable read-only memory (EPROM), electrically erasable PROM(EEPROM), registers, and so forth, including combinations thereof.

Data 733 and instructions 735 may be stored in the memory 731. Theinstructions 735 may include one or more programs, routines,sub-routines, functions, procedures, code, etc. The instructions 735 mayinclude a single computer-readable statement or many computer-readablestatements. The instructions 735 may be executable by the processor 747to implement the method 200 described above and/or one or more of thefunctions described in connection with FIGS. 1-6. Executing theinstructions 735 may involve the use of the data 733 that is stored inthe memory 731. FIG. 7 shows some instructions 735 a and data 733 abeing loaded into the processor 747.

The wireless communication device 749 may also include a transmitter 743and a receiver 745 to allow transmission and reception of signalsbetween the wireless communication device 749 and a remote location(e.g., a base station). The transmitter 743 and receiver 745 may becollectively referred to as a transceiver 741. An antenna 739 may beelectrically coupled to the transceiver 741. The wireless communicationdevice 749 may also include (not shown) multiple transmitters, multiplereceivers, multiple transceivers and/or multiple antennas.

The various components of the wireless communication device 749 may becoupled together by one or more buses, which may include a power bus, acontrol signal bus, a status signal bus, a data bus, etc. Forsimplicity, the various buses are illustrated in FIG. 7 as a bus system737.

In the above description, reference numbers have sometimes been used inconnection with various terms. Where a term is used in connection with areference number, this may be meant to refer to a specific element thatis shown in one or more of the Figures. Where a term is used without areference number, this may be meant to refer generally to the termwithout limitation to any particular Figure.

The term “determining” encompasses a wide variety of actions and,therefore, “determining” can include calculating, computing, processing,deriving, investigating, looking up (e.g., looking up in a table, adatabase or another data structure), ascertaining and the like. Also,“determining” can include receiving (e.g., receiving information),accessing (e.g., accessing data in a memory) and the like. Also,“determining” can include resolving, selecting, choosing, establishingand the like.

The phrase “based on” does not mean “based only on,” unless expresslyspecified otherwise. In other words, the phrase “based on” describesboth “based only on” and “based at least on.”

The term “processor” should be interpreted broadly to encompass ageneral purpose processor, a central processing unit (CPU), amicroprocessor, a digital signal processor (DSP), a controller, amicrocontroller, a state machine, and so forth. Under somecircumstances, a “processor” may refer to an application specificintegrated circuit (ASIC), a programmable logic device (PLD), a fieldprogrammable gate array (FPGA), etc. The term “processor” may refer to acombination of processing devices, e.g., a combination of a digitalsignal processor (DSP) and a microprocessor, a plurality ofmicroprocessors, one or more microprocessors in conjunction with adigital signal processor (DSP) core, or any other such configuration.

The term “memory” should be interpreted broadly to encompass anyelectronic component capable of storing electronic information. The termmemory may refer to various types of processor-readable media such asrandom access memory (RAM), read-only memory (ROM), non-volatile randomaccess memory (NVRAM), programmable read-only memory (PROM), erasableprogrammable read-only memory (EPROM), electrically erasable PROM(EEPROM), flash memory, magnetic or optical data storage, registers,etc. Memory is said to be in electronic communication with a processorif the processor can read information from and/or write information tothe memory. Memory that is integral to a processor is in electroniccommunication with the processor.

The terms “instructions” and “code” should be interpreted broadly toinclude any type of computer-readable statement(s). For example, theterms “instructions” and “code” may refer to one or more programs,routines, sub-routines, functions, procedures, etc. “Instructions” and“code” may comprise a single computer-readable statement or manycomputer-readable statements.

The functions described herein may be implemented in software orfirmware being executed by hardware. The functions may be stored as oneor more instructions on a computer-readable medium. The terms“computer-readable medium” or “computer-program product” refers to anytangible storage medium that can be accessed by a computer or aprocessor. By way of example, and not limitation, a computer-readablemedium may include RAM, ROM, EEPROM, CD-ROM or other optical diskstorage, magnetic disk storage or other magnetic storage devices, or anyother medium that can be used to carry or store desired program code inthe form of instructions or data structures and that can be accessed bya computer. Disk and disc, as used herein, includes compact disc (CD),laser disc, optical disc, digital versatile disc (DVD), floppy disk andBlu-ray® disc, where disks usually reproduce data magnetically, whilediscs reproduce data optically with lasers. It should be noted that acomputer-readable medium may be tangible and non-transitory. The term“computer-program product” refers to a computing device or processor incombination with code or instructions (e.g., a “program”) that may beexecuted, processed or computed by the computing device or processor. Asused herein, the term “code” may refer to software, instructions, codeor data that is/are executable by a computing device or processor.

Software or instructions may also be transmitted over a transmissionmedium. For example, if the software is transmitted from a website,server, or other remote source using a coaxial cable, fiber optic cable,twisted pair, digital subscriber line (DSL), or wireless technologiessuch as infrared, radio, and microwave, then the coaxial cable, fiberoptic cable, twisted pair, DSL, or wireless technologies such asinfrared, radio, and microwave are included in the definition oftransmission medium.

The methods disclosed herein comprise one or more steps or actions forachieving the described method. The method steps and/or actions may beinterchanged with one another without departing from the scope of theclaims. In other words, unless a specific order of steps or actions isrequired for proper operation of the method that is being described, theorder and/or use of specific steps and/or actions may be modifiedwithout departing from the scope of the claims.

It is to be understood that the claims are not limited to the preciseconfiguration and components illustrated above. Various modifications,changes and variations may be made in the arrangement, operation anddetails of the systems, methods, and apparatus described herein withoutdeparting from the scope of the claims.

What is claimed is:
 1. A method for wireless communication, comprising:receiving a signal that is pattern-mapped and Gaussian frequency-shiftkeying (GFSK) modulated; and performing a joint demapping anddemodulation of the received signal based on a stored accumulated phase,wherein performing the joint demapping and demodulation of the receivedsignal comprises performing a combined matched filtering and phaserotation of the received signal.
 2. The method of claim 1, furthercomprising updating the stored accumulated phase based on the jointdemapping and demodulation.
 3. The method of claim 1, wherein thematched filtering determines the pattern mapping of the received signal,and the phase rotation of the received signal is based on the storedaccumulated phase.
 4. The method of claim 3, wherein the storedaccumulated phase is determined from an output of the combined matchedfiltering and phase rotation.
 5. The method of claim 3, whereinperforming a combined matched filtering and phase rotation of thereceived signal comprises: performing phase rotation using the storedaccumulated phase to compensate for a phase of the received signal; andperforming matched filtering using a resulting phase of the phaserotation to determine an output bit.
 6. The method of claim 3, whereinthe phase rotation based on the stored accumulated phase occurs beforematched filtering.
 7. The method of claim 3, wherein matched filteringoccurs before the phase rotation based on the stored accumulated phase.8. The method of claim 1, wherein the stored accumulated phase is fedback to perform phase rotation of the received signal.
 9. The method ofclaim 1, performing the joint demapping and demodulation of the receivedsignal further comprises generating a soft input for a Viterbi decoder.10. A wireless communication device, comprising: a receiver configuredto receive a signal that is pattern-mapped and Gaussian frequency-shiftkeying (GFSK) modulated; and a joint demodulator/demapper configured toperform a joint demapping and demodulation of the received signal basedon a stored accumulated phase, wherein performing the joint demappingand demodulation of the received signal comprises performing a combinedmatched filtering and phase rotation of the received signal.
 11. Thewireless communication device of claim 10, wherein the jointdemodulator/demapper is further configured to update the storedaccumulated phase based on the joint demapping and demodulation.
 12. Thewireless communication device of claim 10, wherein the matched filteringdetermines the pattern mapping of the received signal, and the phaserotation of the received signal is based on the stored accumulatedphase.
 13. The wireless communication device of claim 12, wherein thestored accumulated phase is determined from an output of the combinedmatched filtering and phase rotation.
 14. The wireless communicationdevice of claim 12, wherein performing a combined matched filtering andphase rotation of the received signal comprises: performing phaserotation using the stored accumulated phase to compensate for a phase ofthe received signal; and performing matched filtering using a resultingphase of the phase rotation to determine an output bit.
 15. The wirelesscommunication device of claim 12, wherein the phase rotation based onthe stored accumulated phase occurs before matched filtering.
 16. Thewireless communication device of claim 12, wherein matched filteringoccurs before the phase rotation based on the stored accumulated phase.17. The wireless communication device of claim 10, wherein the storedaccumulated phase is fed back to perform phase rotation of the receivedsignal.
 18. An apparatus for wireless communication, comprising: meansfor receiving a signal that is pattern-mapped and Gaussianfrequency-shift keying (GFSK) modulated; and means for performing ajoint demapping and demodulation of the received signal based on astored accumulated phase, wherein the means for performing the jointdemapping and demodulation of the received signal comprise means forperforming a combined matched filtering and phase rotation of thereceived signal.
 19. The apparatus of claim 18, further comprising meansfor updating the stored accumulated phase based on the joint demappingand demodulation.
 20. The apparatus of claim 18, wherein the matchedfiltering determines the pattern mapping of the received signal, and thephase rotation of the received signal is based on the stored accumulatedphase.
 21. The apparatus of claim 20, wherein the stored accumulatedphase is determined from an output of the combined matched filtering andphase rotation.
 22. The apparatus of claim 20, wherein the means forperforming a combined matched filtering and phase rotation of thereceived signal comprise: means for performing phase rotation using thestored accumulated phase to compensate for a phase of the receivedsignal; and means for performing matched filtering using a resultingphase of the phase rotation to determine an output bit.
 23. Theapparatus of claim 20, wherein matched filtering occurs before the phaserotation based on the stored accumulated phase.
 24. The apparatus ofclaim 18, wherein the stored accumulated phase is fed back to performphase rotation of the received signal.
 25. A computer-program productfor wireless communication, comprising a non-transitory tangiblecomputer-readable medium having instructions thereon, the instructionscomprising: code for causing a wireless communication device to receivea signal that is pattern-mapped and Gaussian frequency-shift keying(GFSK) modulated; and code for causing the wireless communication deviceto perform a joint demapping and demodulation of the received signalbased on a stored accumulated phase, wherein the code for causing thewireless communication device to perform the joint demapping anddemodulation of the received signal comprises code for causing thewireless communication device to perform a combined matched filteringand phase rotation of the received signal.
 26. The computer-programproduct of claim 25, further comprising code for causing the wirelesscommunication device to update the stored accumulated phase based on thejoint demapping and demodulation.
 27. The computer-program product ofclaim 25, wherein the matched filtering determines the pattern mappingof the received signal, and the phase rotation of the received signal isbased on the stored accumulated phase.
 28. The computer-program productof claim 27, wherein the stored accumulated phase is determined from anoutput of the combined matched filtering and phase rotation.
 29. Thecomputer-program product of claim 27, wherein the code for causing thewireless communication device to perform a combined matched filteringand phase rotation of the received signal comprises: code for causingthe wireless communication device to perform phase rotation using thestored accumulated phase to compensate for a phase of the receivedsignal; and code for causing the wireless communication device toperform matched filtering using a resulting phase of the phase rotationto determine an output bit.
 30. The computer-program product of claim25, wherein the stored accumulated phase is fed back to perform phaserotation of the received signal.